Question

In the reaction, \(3 \mathrm{H}_{2}+\mathrm{N}_{2} \longrightarrow 2 \mathrm{NH}_{3}\), how does the rate of disappearance of hydrogen compare to the rate of disappearance of nitrogen? How does the rate of appearance of \(\mathrm{NH}_{3}\) compare to the rate of disappearance of nitrogen?

Short answer

Hydrogen gas disappears 3 times as fast as nitrogen gas. The rate of appearance of ammonia is twice the rate of disappearance of nitrogen.

Step-by-step solution

Understanding the Reaction

The reaction given is a chemical equation that shows the formation of ammonia (NH3) from nitrogen (N2) and hydrogen (H2) gas. According to the balanced equation, 3 moles of hydrogen gas reacts with 1 mole of nitrogen gas to produce 2 moles of ammonia.

Comparing Rates of Disappearance

The rate of disappearance of a reactant in a chemical reaction is proportional to its stoichiometric coefficient in the balanced equation. The stoichiometric coefficient of hydrogen is 3, and the stoichiometric coefficient of nitrogen is 1. Therefore, hydrogen disappears 3 times as fast as nitrogen.

Comparing Rates of Appearance and Disappearance

The rate of appearance of the product in a chemical reaction can also be related to the stoichiometric coefficients. For every mole of nitrogen that reacts, 2 moles of ammonia are produced. Thus, the rate of appearance of ammonia is twice the rate of disappearance of nitrogen.

Key concepts

Chemical Equation Balancing

Balancing chemical equations involves ensuring that the number of atoms for each element is equal on both sides of the equation. This is crucial because it reflects the Conservation of Mass, which states that in a chemical reaction, matter is neither created nor destroyed. Understanding this principle helps to accurately predict the relationship between the reactants and products.

For instance, in the synthesis of ammonia, the balanced equation is:
\(3 \mathrm{H}_2 + \mathrm{N}_2 \longrightarrow 2 \mathrm{NH}_3\).

This balance tells us that three hydrogen molecules (\(H_2\)) react with one nitrogen molecule (\(N_2\)) to form two ammonia molecules (\(NH_3\)). If the equation were unbalanced, it would be difficult to accurately compare the rates of disappearance or formation of different species involved in the reaction.

Stoichiometry

Stoichiometry is the quantitative relationship between the amounts of reactants and products in a chemical reaction. It is based on the balanced chemical equation and allows us to calculate how much of a chemical is consumed or produced.

In the context of the ammonia synthesis reaction, stoichiometry tells us that for every three moles of hydrogen gas consumed, one mole of nitrogen gas is consumed, and two moles of ammonia are produced. These proportions are critical in determining the relative rates at which reactants are used up and products are formed. Understanding stoichiometry not only helps students solve problems related to chemical reactions but also provides a foundation for topics like yield and purity in analytical chemistry.

Reaction Kinetics

Reaction kinetics examines the rates of chemical reactions and the factors that affect these rates. It is an essential concept in understanding how quickly a reaction proceeds. Factors such as concentration, temperature, surface area, and catalysts can influence the rate at which reactants are converted into products.

The rate of a reaction is commonly expressed in terms of the rate of change of concentration of a reactant or product over time. For example, in the ammonia synthesis reaction, the disappearance of hydrogen and nitrogen and the appearance of ammonia occur at rates that can be expressed based on the stoichiometric coefficients from the balanced equation.
Reaction kinetics can be complex and may involve concepts such as reaction order and rate laws, which provide a deeper understanding of the mechanism and speed of reactions.

Ammonia Synthesis

Ammonia synthesis refers to the chemical process of producing ammonia, primarily through the Haber-Bosch process. This process combines nitrogen from the air with hydrogen derived mainly from natural gas (methane) into ammonia. The ammonia synthesis reaction is a key example used in education to illustrate how understanding the balance of chemical equations, stoichiometry, and reaction kinetics is essential in industrial chemistry.

In the balanced equation for ammonia synthesis (\(3 \mathrm{H}_2 + \mathrm{N}_2 \longrightarrow 2 \mathrm{NH}_3\)), not only is the stoichiometry of the reaction important for determining the rates of reaction, but so are the conditions under which the reaction occurs. These include high pressure and the presence of a catalyst, which significantly increase the rate of production of ammonia, illustrating the practical application of chemical principles in a real-world industrial process.